Subscript[r, 1][
l_] = \[Sqrt]2 Sin[\[Pi] l] {0, (Sin^2)[(\[Pi] l)/2], (
Cos^2)[(\[Pi] l)/2]};
Subscript[r, 2][
l_] = \[Sqrt]2 Sin[\[Pi] l] {(Sin^2)[(\[Pi] l)/2], (
Cos^2)[(\[Pi] l)/2], 0};
R[l_] = (1 - l)* Subscript[r, 1][l] + l *Subscript[r, 2][l];
ParametricPlot3D[R[l], {l, 0, 1}]

Sin^2[x]等改成Sin[x]^2
Subscript[r, 1][
l_] = \[Sqrt]2 Sin[\[Pi] l] {0, Sin[(\[Pi] l)/2]^2,
Cos[(\[Pi] l)/2]^2};
Subscript[r, 2][
l_] = \[Sqrt]2 Sin[\[Pi] l] {Sin[(\[Pi] l)/2]^2,
Cos[(\[Pi] l)/2]^2, 0};
R[l_] = (1 - l)*Subscript[r, 1][l] + l*Subscript[r, 2][l];
ParametricPlot3D[R[l], {l, 0, 1}]